According to the results of accelerated tests of acidification corrosion depth and compressive strength of concretes subjected to sulfuric acid environments, the acidification depth laws of concretes were predicted based on the grey system theory. Thus, the remaining compressive strength was calculated when the acidification depth reached the protection layer thickness of concrete structures, which indicates that the limit state of durability failure can be defined based on strength degradation, and the calculation process was illustrated by an example. The calculated results show that the remaining compressive strength values in the durability failure limit state for the concrete structures exposed to pH=2 and 3 sulfuric acid water environments and wet-dry cyclic sulfuric acid environment with pH=2 are 74%, 72%, and 80% of initial strength, respectively. The method provides references for the durability evaluation of concrete structure design under the acidic environments.